Odd-frequency Cooper pairs and zero-energy surface bound states in superfluid 3He

We study the odd-frequency Cooper pairs formed near the surface of superfluid 3He. The odd-frequency pair amplitude is closely related to the local density of states in the low-energy limit. We derive a formula relating explicitly the two quantities. This formula holds for an arbitrary boundary condition at the surface. We also present some numerical results on the surface odd-frequency pair amplitude in superfluid 3He-B. Those analytical and numerical results allow one to interpret the midgap surface density of states, observed recently by transverse acoustic impedance measurements on superfluid 3He-B, as the manifestation of the surface odd-frequency state.